13 citations · 46 across the 15 of their papers we have counts for
15 papers
Compactness phenomena in HOD and the Optimality of Magidor's Covering theorem
Tom Benhamou, James Cummings, Yair Hayut +2
We continue the study of compactness phenomena between the set-theoretic universe and initiated by Goldberg--Poveda \cite{GolPov}. We focus on compactness phenomena…
On the Intermediate Models of Strongly Compact Prikry Forcing
Tom Benhamou, Sebastiano Thei, Ben-Zion Weltsch
We analyze the intermediate models of the strongly compact Prikry forcing. We exhibit a simple combinatorial property which, for a given supercompact cardinal , characterize the…
Applications of the Magidor Iteration to Ultrafilter Theory
Tom Benhamou, Gabriel Goldberg
We characterize sums of normal ultrafilters after the Magidor iteration (product) of Prikry forcings over a discrete set of measurable cardinals. We apply this to show that the wea…
Non-Normal Magidor-Radin Types of Forcings
Tom Benhamou, Alejandro Poveda
We develop the non-normal variations of two classical Prikry-type forcings; namely, Magidor and Radin forcings. We generalize the fact that the non-normal Prikry forcing is a proje…
Transferring Compactness
Tom Benhamou, Jing Zhang
We demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible…
The Galvin property under the Ultrapower Axiom
Tom Benhamou, Gabriel Goldberg
We continue the study of the Galvin property from \cite{bgs} and \cite{Benhamou2}. In particular, we deepen the connection between certain diamond-like principles and non-Galvin ul…
Saturation Properties of Ultrafilters in Canonical Inner Models
Tom Benhamou
We improve Galvin's Theorem for ultrafilters which are p-point limits of p-points. This implies that in all the canonical inner models up to a superstrong cardinal, every -compl…
Non-Galvin Filters
Tom Benhamou, Shimon Garti, Moti Gitik +1
We address the question of the consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions \cite[Questions 7.8,7.9]{TomM…
Galvin's property at large cardinals and an application to partition calculus
Tom Benhamou, Shimon Garti, Alejandro Poveda
In the first part of this paper, we explore the possibility for a very large cardinal to carry a -complete ultrafilter without Galvin's property. In this context, we prove t…
On Cohen and Prikry Forcing Notions
Tom Benhamou, Moti Gitik
We show that it is possible to add Cohen subsets to with a Prikry forcing over . This answers a question from \cite{HayutBenhanouGitik}. A strengthening of non-Galvin…
Negating the Galvin Property
Tom Benhamou, Shimon Garti, Alejandro Poveda
We prove that Galvin's property consistently fails at successors of strong limit singular cardinals. We also prove the consistency of this property failing at every successor of a…
The Variety of Projection of a Tree-Prikry Forcing
Tom Benhamou, Moti Gitik, Yair Hayut
We study which -distributive forcing notions of size can be embedded into tree Prikry forcing notions with -complete ultrafilters under various large cardinal assumptions…
Intermediate Models of Magidor-Radin Forcing- Part II
Tom Benhamou, Moti Gitik
We continue the work done by the authors and before that by the second author, Kanovei and koepke. We prove that for every set of ordinals in a Magidor-Radin generic extension…
Intermediate Models in Magidor-Radin Forcing- Part I
Tom Benhamou, Moti Gitik
We continue the work done by Gitik, Kanovei, Koepke, and later by the authors. We prove that for every set in a Magidor-Radin generic extension using a coherent sequence such t…
Sets in Prikry and Magidor Generic Extensions
Tom Benhamou, Moti Gitik
We continue Gitik, Kanovei and Koepke's work and study sets in generic extensions by the Magidor forcing and by the Prikry forcing with non-normal ultrafilters.